Drawing circumcircle of BCD turns the problem into a cevian model 20,10,30,20,120-x,x-20.General solution of that kind of cevian model listed here: http://geomania.org/forum/fantezi-geometri/ucgen-icerisinde-p-noktasi-model-4-3/ but in Turkish. But you can follow via pictures.Remember that in a cevian model, some angles can be interchanged.